JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 1

If the domain of the function $f(x)=\frac{\cos^{-1}\sqrt{x^{2}-x+1}}{\sqrt{\sin^{-1}\left(\frac{2x-1}{2}\right)}}$ is the interval $(\alpha,\beta]$, then $\alpha+\beta$ is equal to :

Functions

$1$$2$$\frac{1}{2}$$\frac{3}{2}$

JEE Main 2021 (Online) 31st August Evening ShiftQuestion 2

The domain of the function $f(x)=\sin^{-1}\left(\frac{3x^{2}+x-1}{(x-1)^{2}}\right)+\cos^{-1}\left(\frac{x-1}{x+1}\right)$ is :

Functions

$\left[0,\frac{1}{4}\right]$$\left[0,\frac{1}{2}\right]$$\left[\frac{1}{4},\frac{1}{2}\right]\cup\{0\}$$[-2,0]\cup\left[\frac{1}{4},\frac{1}{2}\right]$

JEE Main 2021 (Online) 25th July Evening ShiftQuestion 3

If $[x]$ be the greatest integer less than or equal to $x$, then $\sum_{n=8}^{100}\left[\frac{(-1)^{n}n}{2}\right]$ is equal to :

Functions

$-2$$0$$2$$4$

JEE Main 2023 (Online) 11th April Evening ShiftQuestion 4

Let $f$ and $g$ be two functions defined by $f(x)=\begin{cases}x+1, & x<0\\ |x-1|, & x\ge0\end{cases}$ and $g(x)=\begin{cases}x+1, & x<0\\ 1, & x\ge0\end{cases}$. Then $(g\circ f)(x)$ is

Functions

differentiable everywherenot continuous at $x=-1$continuous everywhere but not differentiable at $x=1$continuous everywhere but not differentiable exactly at one point

JEE Main 2025 (Online) 4th April Morning ShiftQuestion 5

Let $f,g:(1,\infty)\to\mathbb{R}$ be defined as $f(x)=\frac{2x+3}{5x+2}$ and $g(x)=\frac{2-3x}{1-x}$. If the range of the function $f\circ g:[2,4]\to\mathbb{R}$ is $[\alpha,\beta]$, then $\frac{1}{\beta-\alpha}$ is equal to

Functions

$2$$29$$56$$68$